The late, who worked for the BBC Media Action charity was found stabbed on Friday, November 19 shortly after an emergency alarm was activated in her room.
Police said the window to her eighth-floor hotel room had been broken and the body of a man Mitchell had been with earlier was found on the ground below.
Officials aware of the probe say Henry Tamati Mauti, the Kenyan man who is suspected to be the killer of Mitchell, was known to her and was helping her move around.
The man, a graduate of United States International University (USIU), had studied radiography. The motive of the incident is yet to be established.
The BBC described Mitchell as “positive, fun, driven and extremely talented” and said her work made a huge difference to communities across the globe, addressing poverty and inequality.
The broadcaster said it is working with the Government to establish the circumstances around Mitchell’s death, although it believes it was not linked to her work.
Mitchell’s brother paid tribute to her and said: “Kate was a deeply beloved daughter, sister and friend, and we are only beginning to realise the magnitude of her loss.
Kate loved her work and was tireless in her efforts to make the world a better place. She leaves behind many, many beloved friends and colleagues around the world.
We want to extend our sympathies to everyone who knew, worked with and loved her, and our sincere thanks for the many messages of comfort we have received.”